However, minority governments or oversized coalitions occur more than exceptionally, too.
Mathematical indexes reflect these rules only partially. One way of defining the index of power is the probability of being in the winning coalition represented by the Banzhaf and Shapley-Shubik indices. Another method is based on the political nearness principle measured in the Euclidean space. Power indices constitute important description of potentials in any kind of social games. In coalition building their application is still very limited. It is based on innumerable number of factors that influence the social outcome. Nevertheless, they are used in projecting assemblies consisting of subject of different size that are supposed to have the same power per vote. One example of application for all: in the United States presidential elections more votes is given to smaller states than their share of population in the union. This means that in the District of Columbia or Wyoming one presidential elector corresponds with about 60-70,000 voters, whereas in Florida, Ohio or Illinois this number is about three times higher (200-240,000). Unfair? This inproportionality was created in order to give the same power to each vote taking into account the coalition-building potential of this vote. Therefore, larger states are represented by fewer electors with the intention of lessening their high coalition formation potential. The same approach is used in the European Parliament, for example.